| 35-XX | | Prev: 34 | Up: Top | Next: 37 | |
| Partial differential equations [xref: 22E05, 58J05, 58Jxx] |
35-00
| General reference works (handbooks, dictionaries, bibliographies, etc.)
| 35-01
| Instructional exposition (textbooks, tutorial papers, etc.)
| 35-02
| Research exposition (monographs, survey articles)
| 35-03
| Historical (must also be assigned at least one classification number from Section 01)
| 35-04
| Explicit machine computation and programs (not the theory of computation or programming)
| 35-06
| Proceedings, conferences, collections, etc.
| |
35Axx
| General theory
[xref: 37Kxx]
| 35A05 |
General existence and uniqueness theorems
| 35A07 |
Local existence and uniqueness theorems [See also 35Hxx, 35Sxx]
| 35A08 |
Fundamental solutions
| 35A10 |
Cauchy-Kovalevskaya theorems
| 35A15 |
Variational methods
| 35A17 |
Parametrices
| 35A18 |
Wave front sets
| 35A20 |
Analytic methods, singularities
| 35A21 |
Propagation of singularities
| 35A22 |
Transform methods (e.g. integral transforms)
[xref: 58J72]
| 35A25 |
Other special methods
| 35A27 |
Microlocal methods; methods of sheaf theory and homological algebra in PDE [See also 32C38, 58J15]
[xref: 32C38]
| 35A30 |
Geometric theory, characteristics, transformations [See also 58J70, 58J72]
[xref: 58J70]
| 35A35 |
Theoretical approximation to solutions {For numerical analysis, see 65Mxx, 65Nxx}
| 35A99 |
None of the above, but in this section
| |
35Bxx
| Qualitative properties of solutions
[xref: 35Kxx, 37Lxx]
| 35B05 |
General behavior of solutions of PDE (comparison theorems; oscillation, zeros and growth of solutions; mean value theorems)
| 35B10 |
Periodic solutions
| 35B15 |
Almost periodic solutions
| 35B20 |
Perturbations
| 35B25 |
Singular perturbations
| 35B27 |
Homogenization; partial differential equations in media with periodic structure [See also 74Qxx, 76M50]
| 35B30 |
Dependence of solutions of PDE on initial and boundary data, parameters [See also 37Cxx]
| 35B32 |
Bifurcation [See also 37Gxx, 37K50]
[xref: 58J55]
| 35B33 |
Critical exponents
| 35B34 |
Resonances
| 35B35 |
Stability, boundedness
| 35B37 |
PDE in connection with control problems [See also 49J20, 49K20, 93C20]
[xref: 93C20]
| 35B38 |
Critical points
| 35B40 |
Asymptotic behavior of solutions
| 35B41 |
Attractors
| 35B42 |
Inertial manifolds
| 35B45 |
A priori estimates
| 35B50 |
Maximum principles
| 35B60 |
Continuation and prolongation of solutions of PDE [See also 58A15, 58A17, 58Hxx]
| 35B65 |
Smoothness and regularity of solutions of PDE
| 35B99 |
None of the above, but in this section
| |
35Cxx
| Representations of solutions
| 35C05 |
Solutions in closed form
| 35C10 |
Series solutions, expansion theorems
| 35C15 |
Integral representations of solutions of PDE
| 35C20 |
Asymptotic expansions
| 35C99 |
None of the above, but in this section
| |
35Dxx
| Generalized solutions of partial differential equations
[xref: 35Kxx]
| 35D05 |
Existence of generalized solutions
| 35D10 |
Regularity of generalized solutions
| 35D99 |
None of the above, but in this section
| |
35Exx
| Equations and systems with constant coefficients [See also 35N05]
| 35E05 |
Fundamental solutions
| 35E10 |
Convexity properties
| 35E15 |
Initial value problems
| 35E20 |
General theory
| 35E99 |
None of the above, but in this section
| |
35Fxx
| General first-order equations and systems
| 35F05 |
General theory of linear first-order PDE
| 35F10 |
Initial value problems for linear first-order PDE, linear evolution equations
| 35F15 |
Boundary value problems for linear first-order PDE
| 35F20 |
General theory of nonlinear first-order PDE
| 35F25 |
Initial value problems for nonlinear first-order PDE, nonlinear evolution equations
| 35F30 |
Boundary value problems for nonlinear first-order PDE
| 35F99 |
None of the above, but in this section
| |
35Gxx
| General higher-order equations and systems
| 35G05 |
General theory of linear higher-order PDE
| 35G10 |
Initial value problems for linear higher-order PDE, linear evolution equations
| 35G15 |
Boundary value problems for linear higher-order PDE
| 35G20 |
General theory of nonlinear higher-order PDE
| 35G25 |
Initial value problems for nonlinear higher-order PDE, nonlinear evolution equations
| 35G30 |
Boundary value problems for nonlinear higher-order PDE
| 35G99 |
None of the above, but in this section
| |
35Hxx
| Close-to-elliptic equations
[xref: 35A07]
| 35H10 |
Hypoelliptic equations
| 35H20 |
Subelliptic equations
| 35H30 |
Quasi-elliptic equations
| 35H99 |
None of the above, but in this section
| |
35Jxx
| Partial differential equations of elliptic type [See also 58Jxx, 58J10, 58J20]
| 35J05 |
Laplace equation, reduced wave equation (Helmholtz), Poisson equation [See also 31Axx, 31Bxx]
[xref: 35Qxx]
| 35J10 |
Schrödinger operator [See also 35Pxx]
[xref: 35Qxx]
| 35J15 |
General theory of second-order, elliptic equations
[xref: 45E05]
| 35J20 |
Variational methods for second-order, elliptic equations
| 35J25 |
Boundary value problems for second-order, elliptic equations
| 35J30 |
General theory of higher-order, elliptic equations [See also 31A30, 31B30]
| 35J35 |
Variational methods for higher-order, elliptic equations
| 35J40 |
Boundary value problems for higher-order, elliptic equations
| 35J45 |
General theory of elliptic systems of PDE
| 35J50 |
Variational methods for elliptic systems
| 35J55 |
Boundary value problems for elliptic systems
| 35J60 |
Nonlinear PDE of elliptic type
| 35J65 |
Nonlinear boundary value problems for linear elliptic PDE; boundary value problems for nonlinear elliptic PDE
| 35J67 |
Boundary values of solutions to elliptic PDE
| 35J70 |
Elliptic partial differential equations of degenerate type
| 35J85 |
Unilateral problems and variational inequalities for elliptic PDE [See also 35R35, 49J40]
| 35J99 |
None of the above, but in this section
| |
35Kxx
| Parabolic equations and systems [See also 35Bxx, 35Dxx, 35R30, 35R35, 58J35]
| 35K05 |
Heat equation
[xref: 35Qxx]
| 35K10 |
General theory of second-order, parabolic equations
| 35K15 |
Initial value problems for second-order, parabolic equations
| 35K20 |
Boundary value problems for second-order, parabolic equations
| 35K25 |
General theory of higher-order, parabolic equations
| 35K30 |
Initial value problems for higher-order, parabolic equations
| 35K35 |
Boundary value problems for higher-order, parabolic equations
| 35K40 |
General theory of parabolic systems of PDE
| 35K45 |
Initial value problems for parabolic systems
| 35K50 |
Boundary value problems for parabolic systems
| 35K55 |
Nonlinear PDE of parabolic type
| 35K57 |
Reaction-diffusion equations
| 35K60 |
Nonlinear boundary value problems for linear parabolic PDE; boundary value problems for nonlinear parabolic PDE
| 35K65 |
Parabolic partial differential equations of degenerate type
| 35K70 |
Ultraparabolic, pseudoparabolic PDE, etc.
| 35K85 |
Unilateral problems and variational inequalities for parabolic PDE [See also 35R35, 49J40]
| 35K90 |
Abstract parabolic evolution equations
[xref: 47J35, 58D25]
| 35K99 |
None of the above, but in this section
| |
35Lxx
| Partial differential equations of hyperbolic type [See also 58J45]
[xref: 58J45]
| 35L05 |
Wave equation
[xref: 35Qxx]
| 35L10 |
General theory of second-order, hyperbolic equations
| 35L15 |
Initial value problems for second-order, hyperbolic equations
| 35L20 |
Boundary value problems for second-order, hyperbolic equations
| 35L25 |
General theory of higher-order, hyperbolic equations
| 35L30 |
Initial value problems for higher-order, hyperbolic equations
| 35L35 |
Boundary value problems for higher-order, hyperbolic equations
| 35L40 |
General theory of hyperbolic systems of first-order PDE
| 35L45 |
Initial value problems for hyperbolic systems of first-order PDE
| 35L50 |
Boundary value problems for hyperbolic systems of first-order PDE
| 35L55 |
Hyperbolic systems of higher-order PDE
| 35L60 |
Nonlinear first-order PDE of hyperbolic type
[xref: 76N10]
| 35L65 |
Conservation laws
[xref: 76N10]
| 35L67 |
Shocks and singularities [See also 58Kxx, 76L05]
[xref: 76L05]
| 35L70 |
Nonlinear second-order PDE of hyperbolic type
| 35L75 |
Nonlinear hyperbolic PDE of higher ($\gtr 2$) order
| 35L80 |
Hyperbolic PDE of degenerate type
| 35L82 |
Pseudohyperbolic equations
| 35L85 |
Unilateral problems; variational inequalities for hyperbolic PDE [See also 35R35, 49J40]
| 35L90 |
Abstract hyperbolic evolution equations
[xref: 47J35, 58D25]
| 35L99 |
None of the above, but in this section
| |
35Mxx
| Partial differential equations of special type (mixed, composite, etc.) {For degenerate types, see 35J70, 35K65, 35L80}
| 35M10 |
PDE of mixed type
| 35M20 |
PDE of composite type
| 35M99 |
None of the above, but in this section
| |
35Nxx
| Overdetermined systems [See also 58Hxx, 58Jxx, 58J10, 58J15]
[xref: 58J10]
| 35N05 |
Overdetermined systems with constant coefficients
[xref: 35Exx]
| 35N10 |
Overdetermined systems with variable coefficients (general)
| 35N15 |
$\overline\partial$-Neumann problem and generalizations; formal complexes [See also 32W05, 32W10, 58J10]
| 35N99 |
None of the above, but in this section
| |
35Pxx
| Spectral theory and eigenvalue problems for partial differential operators [See also 47Axx, 47Bxx, 47F05]
[xref: 35J10, 45C05, 47F05, 58J50]
| 35P05 |
General spectral theory of PDE
| 35P10 |
Completeness of eigenfunctions, eigenfunction expansions for PDO
| 35P15 |
Estimation of eigenvalues, upper and lower bounds
| 35P20 |
Asymptotic distribution of eigenvalues and eigenfunctions for PDO
| 35P25 |
Scattering theory for PDE [See also 47A40]
[xref: 47A40, 81Uxx]
| 35P30 |
Nonlinear eigenvalue problems, nonlinear spectral theory for PDO
| 35P99 |
None of the above, but in this section
| |
35Qxx
| Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05]
[xref: 37Kxx, 37Lxx, 47J35]
| 35Q05 |
Euler-Poisson-Darboux equation and generalizations
| 35Q15 |
Riemann-Hilbert problems [See also 30E25, 31A25, 31B20]
| 35Q30 |
Stokes and Navier-Stokes equations [See also 76D05, 76D07, 76N10]
[xref: 76B15, 76D03, 76D05, 76N10]
| 35Q35 |
Other equations arising in fluid mechanics
[xref: 76B03, 76D03]
| 35Q40 |
Equations from quantum mechanics
| 35Q51 |
Solitons [See also 37K40]
[xref: 76B25]
| 35Q53 |
KdV-like equations (Korteweg-de Vries, Burgers, sine-Gordon, sinh-Gordon, etc.) [See also 37K10]
[xref: 76B15]
| 35Q55 |
NLS-like (nonlinear Schrödinger) equations [See also 37K10]
| 35Q58 |
Other completely integrable equations [See also 37J35, 37K10]
| 35Q60 |
Equations of electromagnetic theory and optics
| 35Q72 |
Other equations from mechanics
| 35Q75 |
PDE in relativity
| 35Q80 |
Applications of PDE in areas other than physics
| 35Q99 |
None of the above, but in this section
| |
35Rxx
| Miscellaneous topics involving partial differential equations {For equations on manifolds, see 58Jxx; for manifolds of solutions, see 58Bxx; for stochastic PDEs, see also 60H15}
| 35R05 |
PDE with discontinuous coefficients or data
| 35R10 |
Partial functional-differential or differential-difference equations, with or without deviating arguments
[xref: 45K05, 47G20]
| 35R12 |
Impulsive partial differential equations
| 35R15 |
Partial differential equations on infinite-dimensional (e.g. function) spaces (=PDE in infinitely many variables) [See also 46Gxx, 58D25]
[xref: 58D25]
| 35R20 |
Partial operator-differential equations (i.e. PDE on finite-dimensional spaces for abstract space valued functions) [See also 34Gxx, 47A50, 47D03, 47D06, 47D09, 47H20, 47Jxx]
[xref: 47J35]
| 35R25 |
Improperly posed problems for PDE
| 35R30 |
Inverse problems (undetermined coefficients, etc.) for PDE
[xref: 35Kxx, 86A22]
| 35R35 |
Free boundary problems for PDE
[xref: 35J85, 35K85, 35Kxx, 35L85]
| 35R45 |
Partial differential inequalities
| 35R50 |
Partial differential equations of infinite order
| 35R60 |
Partial differential equations with randomness [See also 60H15]
[xref: 37L55, 58J65, 60H15]
| 35R70 |
PDE with multivalued right-hand sides
| 35R99 |
None of the above, but in this section
| |
35Sxx
| Pseudodifferential operators and other generalizations of partial differential operators [See also 47G30, 58J40]
[xref: 35A07, 47G30, 58J40]
| 35S05 |
General theory of PsDO
| 35S10 |
Initial value problems for PsDO
| 35S15 |
Boundary value problems for PsDO
| 35S30 |
Fourier integral operators
| 35S35 |
Topological aspects: intersection cohomology, stratified sets, etc. [See also 32C38, 32S40, 32S60, 58J15]
| 35S50 |
Paradifferential operators
| 35S99 |
None of the above, but in this section
| |